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Convex and Nonlinear Numerical Optimization (MM25)
Announcements
No lecture on Tue, Nov 5 (due to a conference)
Content
The lecture is organized into two parts.
Part 1 is devoted to convex analysis and programming which play a key role in computational data analysis and also provide the basis for nonconvex problems (Part 2). Keywords: smooth and nonsmooth convex analysis, conjugation and duality, conic programs, operator splitting, deterministic and stochastic convex optimization.
Part 2 is devoted to nonconvex problems with additional structure that enables to design convergent algorithms. Keywords: elementary Riemannian manifolds, retractions, nonpositive curvature, Riemannian means, Kurdyka-Lojasiewicz property and global proximal optimization.
Basic problems from machine learning and computational data analysis illustrate the application of these concepts.
Organization
Place & Time
- Lecture: Tuesday and Friday from 11-13 in seminar room 6 in the Mathematikon (INF 205)
- Exercise class: Thursday 9-11 in seminar room 7 in the Mathematikon (INF 205), the first exercise class will be on 24th of October.
Language
English or German, as the audience requests.
Target Audience
Students of mathematics and scientific computing that are interested numerical optimization, with a focus on applications to data analysis and machine learning.
Prerequisites
Mandatory undergraduate courses on analysis and linear algebra.
Registration
If you wish to attend the lecture and the exercises, please sign up using MÜSLI.
Exercises
Each week there will be an exercise sheet you can voluntarily work on. The exercises will not be collected and corrected, but the solutions will be presented in the exercise class.
Some exercise sheets contain (voluntary) programming exercises, which also will be discussed in the exercise class. We recommend programming the exercises with Python and numpy. A basic understanding of Python and numpy should be sufficient for most exercises.
Lecture Notes
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Table of Contents (Dec 2)
Introduction (update: Oct 18)
Literature
Preliminaries: SVD
Smooth Convex Functions
Nonsmooth Convex Functions, Convex Sets, Optimality (update: Nov 25)
Nonexpansive Operators (update: Nov 25)
Convex Optimisation Algorithms 1
Convex Optimisation Algorithms 2
Exercise Sheets
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